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Two objects have masses of #22 MG# and #23 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #25 m# to #75 m#?

Answer 1

Isabella Alvarez

The change in gravitational potential energy is #=90*10^-5J#

The potential energy per kilogram at a point in a field is known as the gravitational potential.

So the units are #J, "Joules"#

#Phi=-G(M_1M_2)/R#

The universal constant of gravitation is

G is 6.67 * 10^-11 Nm^2 kg^-2.

The masses causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=22MG=22*10^6g=22*10^3kg#

The mass is #M_2=23MG=23*10^6g=23*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=25m#

The distance #R_2=75m#

Consequently,

#Phi_1=(-G*(22*10^3*23*10^3)/25)#

#Phi_2=(-G*(22*10^3*23*10^3)/75)#

Thus,

#Phi_1-Phi_2=(-G*(22*10^3*23*10^3)/25)-(-G*(22*10^3*23*10^3)/75)#

#=22*23*10^6*6.67*10^-11(1/75-1/25)#

#=-90*10^-5J#

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Answer 2

Elena Albarran

The change in gravitational potential energy between the objects is (3.36 \times 10^{14}) joules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.